Geodesic
The Poincaré inequality is an open ended condition
Stephen Keith1 ; Xiao Zhong2
1 Mathematical Sciences Institute<br/>Australian National University<br/>Canberra 0200<br/>Australia
2 Department of Mathematics and Statistics<br/>University of Jyväskylä<br/>Jyväskylä<br/>Finland
Annals of mathematics, Tome 167 (2008) no. 2, pp. 575-599.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Let $p >1$ and let $(X,d,\mu)$ be a complete metric measure space with $\mu$ Borel and doubling that admits a $(1,p)$-Poincaré inequality. Then there exists $\varepsilon >0$ such that $(X,d,\mu)$ admits a $(1,q)$-Poincaré inequality for every $q >p – \varepsilon$, quantitatively.
DOI : 10.4007/annals.2008.167.575

Stephen Keith 1 ; Xiao Zhong 2

1 Mathematical Sciences Institute<br/>Australian National University<br/>Canberra 0200<br/>Australia
2 Department of Mathematics and Statistics<br/>University of Jyväskylä<br/>Jyväskylä<br/>Finland 
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Stephen Keith; Xiao Zhong. The Poincaré inequality is an open ended condition. Annals of mathematics, Tome 167 (2008) no. 2, pp. 575-599. doi : 10.4007/annals.2008.167.575. http://geodesic.mathdoc.fr/articles/10.4007/annals.2008.167.575/

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